# Variation of Resistance with temperature Lab experiment

1. Dec 10, 2011

### eximius

I'm not sure if this is the right place to post this, but it seems to be the best fit.

1. The problem statement, all variables and given/known data
I'm trying to write a lab report about how resistance varies with temperature. I used liquid nitrogen to cool a copper coil and a semiconductor(thermistor) from room temperature to about 120K. I got good results with a linear relationship between the coil resistance and temperature and a linear relationship between ln(R) of the thermistor and 1/T. The temperature was determined using the emf of a thermocouple.

I'm just trying to understand the equations given to us.

2. Relevant equations

R(T) = R_273(1+alpha(T - Tref)) ... coil
R(T) = a*e^(b/T) ... thermistor

3. The attempt at a solution

I've used the first equation to calculate the resistance of the coil and it all seems ok.

But I just don't get the second equation. "a" and "b" are simply stated to be constants.

From some source I found that "a" might be the intercept value on the ln(R) against 1/T graph. So I calculated it as e^(4/5) and b as 2073.68 at 218K. This seemed to match with my measured results. But I still don't know what the constants actually represent.

Is the equation a modified form of the "Steinhart Hart equation"?

Any and all help would be appreciated.

Any and all help would be appreciated

2. Dec 10, 2011

### technician

For the thermistor, if
R = a*e^(b/T) then ln(R) = ln(a) +b/T
So a graph of ln(R) against 1/T should be a straight line with intercept = ln(a) (you seem to realise this.... but be careful, the intercept is ln(a) nota)
The gradient of the straight line will be the constant 'b'. It will have units of temperature
Hope this helps

3. Dec 10, 2011

### eximius

Thanks for the reply it really does help. So it seems that I've done it correctly. But does anyone have any idea of the name of the formula, where it comes from, the names of the a and b constants etc? Am I right in thinking that it's from the "Steinhart Hart equation"?

4. Dec 10, 2011

### technician

Cant help you there !!! I have not heard of that equation.... I will Google and see what comes up.
The main thing is your analysis is good.